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Edward Tufte’s Recommendations Show the data Induce the viewer to think about the substance of the data Avoid distorting what the data have to say Present many numbers in a small space Make large data sets coherent Encourage comparison Reveal the data at several levels of detail Serve a clear purpose Be closely integrated with the statistical and verbal descriptions of the data –Tufte, E R (2001), The Visual Display of Quantitative Information, Graphics Press.

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Tufte’s Points Graphics reveal data. Graphics can be more precise and revealing than conventional statistics. Anscombe’s data –Anscombe, F J (1973) “Graphs in Statistical Analysis”, American Statistician, 27: All four data sets are described by the same linear model. IxIyIixIiyIIIxIIIyIVxIVy

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Demonstration Launch R Set the working directory to Statistics/RSPCMA/Data airpoll

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Convex Hull of Bivariate Data Scatterplots are often used during the calculation of the correlation coefficient of two variables. Used to detect outliers. Convex hull trimming generates a robust estimate of the correlation coefficient. Demonstration –attach(airpoll) –cor(SO2, Mortality)

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Robust Estimation of the Correlation hull

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Chiplot A way of augmenting the scatterplot to spot dependence/independence. See Statistics/RSCMPA/functions.txt chiplot(SO2,Mortality,vlabs=c("SO2", "Mortality") For independent data, the points will be scattered in a horiszontal band centered around 0. Departure from independence here is shown by the points missing from (-0.25,0.25)

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Bivariate Densities The goal of examining a scatterplot is to identify clusters and outliers. Humans are not particularly good at this, so graphical aids help. Adding a bivariate density estimate is good. Histograms are too rough, though.

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Conclusions The purpose of graphics is to aid your intuition. Explore them—the appropriate graphics reflect your questions and the structure of the data. Next week: graphic presentations to avoid, because they mislead you and your audience. Look at the books by Edward Tufte in the library.